Please wait a minute...
Applied Mathematics-A Journal of Chinese Universities  2019, Vol. 34 Issue (2): 184-    DOI: 10.1007/s11766-019-3619-x
    
Existence and Stability of Solutions to Highly Nonlinear Stochastic Differential Delay Equations Driven by G-Brownian Motion
FEI Chen, FEI Wei-yin, YAN Li-tan
1 Glorious Sun School of Business and Management,Donghua University, Shanghai, 200051,China.
2 School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, Anhui 241000,China.
Existence and Stability of Solutions to Highly Nonlinear Stochastic Differential Delay Equations Driven by G-Brownian Motion
FEI Chen, FEI Wei-yin, YAN Li-tan
1 Glorious Sun School of Business and Management,Donghua University, Shanghai, 200051,China.
2 School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, Anhui 241000,China.
 全文: PDF 
摘要： Under linear expectation (or classical probability), the stability for stochastic differential
delay equations (SDDEs), where their coefficients are either linear or nonlinear but
bounded by linear functions, has been investigated intensively. Recently, the stability of highly
nonlinear hybrid stochastic differential equations is studied by some researchers. In this paper,
by using Peng’s G-expectation theory, we first prove the existence and uniqueness of solutions
to SDDEs driven by G-Brownian motion (G-SDDEs) under local Lipschitz and linear growth
conditions. Then the second kind of stability and the dependence of the solutions to G-SDDEs
are studied. Finally, we explore the stability and boundedness of highly nonlinear G-SDDEs.
关键词： stochastic differential delay equation (SDDE);  sublinear expectation;  existence and uniqueness;  G-Brownian motion, stability and boundedness    
Abstract: Under linear expectation (or classical probability), the stability for stochastic differential
delay equations (SDDEs), where their coefficients are either linear or nonlinear but
bounded by linear functions, has been investigated intensively. Recently, the stability of highly
nonlinear hybrid stochastic differential equations is studied by some researchers. In this paper,
by using Peng’s G-expectation theory, we first prove the existence and uniqueness of solutions
to SDDEs driven by G-Brownian motion (G-SDDEs) under local Lipschitz and linear growth
conditions. Then the second kind of stability and the dependence of the solutions to G-SDDEs
are studied. Finally, we explore the stability and boundedness of highly nonlinear G-SDDEs.
Key words: stochastic differential delay equation (SDDE)    sublinear expectation    existence and uniqueness    G-Brownian motion, stability and boundedness
出版日期: 2019-07-03
CLC:  60H10  
服务　　
把本文推荐给朋友
加入引用管理器
E-mail Alert
RSS
作者相关文章　　
FEI Chen
FEI Wei-yin
YAN Li-tan

引用本文:

FEI Chen, FEI Wei-yin, YAN Li-tan. Existence and Stability of Solutions to Highly Nonlinear Stochastic Differential Delay Equations Driven by G-Brownian Motion[J]. Applied Mathematics-A Journal of Chinese Universities, 2019, 34(2): 184-.

FEI Chen, FEI Wei-yin, YAN Li-tan. Existence and Stability of Solutions to Highly Nonlinear Stochastic Differential Delay Equations Driven by G-Brownian Motion. Applied Mathematics-A Journal of Chinese Universities, 2019, 34(2): 184-.

链接本文:

http://www.zjujournals.com/amjcub/CN/10.1007/s11766-019-3619-x    或    http://www.zjujournals.com/amjcub/CN/Y2019/V34/I2/184

[1] Yousef Alnafisah. The implementation of approximate coupling in two-dimensional SDEs with invertible diffusion terms[J]. Applied Mathematics-A Journal of Chinese Universities, 2020, 35(2): 166-183.
[2] ZHENG Jing, TONG Chang-qing, ZHANG Gui-jun. Modeling stochastic mortality with O-U type processes[J]. Applied Mathematics-A Journal of Chinese Universities, 2018, 33(1): 48-58.